A simplified two-dimensional boundary element method with arbitrary uniform mean flow

Abstract

To reduce computational costs, an improved form of the frequency domain boundary element method (BEM) is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation (BIE) representation solves the two-dimensional convected Helmholtz equation (CHE) and its fundamental solution, which must satisfy a new Sommerfeld radiation condition (SRC) in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Greenâs kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole, dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation. Keywords: Two-dimensional convected Helmholtz equation, Two-dimensional convected Greenâs function, Two-dimensional convected boundary element method, Arbitrary uniform mean flow, Two-dimensional acoustic source